In how may different ways can the letters of the word 'PIRATE' be arranged in such a way that the vowels always come together?

Question: In how may different ways can the letters of the word PIRATE be arranged in such a way that the vowels always come together?

Solution:
The word 'PIRATE' contains 6 different letters.
When the vowels IAE are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PRT(IAE).
Now, 4 letters can be arranged in 4! ways
= 24 ways.
The vowels (IAE) can be arranged among themselves in 3! = 6 ways.

∴ Required number of ways = (24 x 6) = 144